Blair, joined by his wife Cherie and culture secretary Tessa Jowell, arrived in Singapore yesterday ahead of his French rival Jacques Chirac.
Although still second favourite behind Paris to win the games, Blair said: "I think it is recognised as a very, very strong bid."
Jacques Rogge, president of the International Olympic Committee, also said the contest between London and Paris was extremely close.
"I even have the feeling without being in the minds of those voting that the difference between the winner and the second-placed candidate may not exceed half-a-dozen votes," he said.
The five shortlisted cities -- Paris, London, New York, Madrid and Moscow -- will be doing their final campaigns over the next two days with the winner to be announced on Wednesday.
New York has pulled out all the stops with former boxing legend Muhammad Ali and former first lady Senator Hilary Clinton, while footballer Laurent Blanc, 1500m champion Michel Jazy and athlete Marie-Jose Perec are turning out for Paris.
Moscow has gymnast Irina Rodnina and Madrid has Spanish prime minister Jose Luis Rodriguez Zapatero representing their final bids.
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